Diffuse relaxation approximation in a heated Fermi system

An expression for the two-particle relaxation time of collective excitations on a distorted Fermi surface in the diffusion approach to kinetic theory is obtained. The general case of momentum-dependent diffusion and drift coefficients is considered. The temperature dependence of the obtained expression is established.

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Diffuse approximation to the kinetic theory in a Fermi system

International Journal of Modern Physics E ◽

10.1142/s0218301315500238 ◽

2015 ◽

Vol 24 (04) ◽

pp. 1550023

Author(s):

V. M. Kolomietz ◽

S. V. Lukyanov

Keyword(s):

Kinetic Theory ◽

Fermi Surface ◽

Wigner Distribution ◽

Fermi System ◽

Relaxation Processes ◽

Momentum Dependence ◽

Wigner Distribution Function ◽

Range Interaction ◽

Interparticle Collisions ◽

Diffuse Approximation

We suggest the diffuse approach to the relaxation processes within the kinetic theory for the Wigner distribution function. The diffusion and drift coefficients are evaluated taking into consideration the interparticle collisions on the distorted Fermi surface. Using the finite range interaction, we show that the momentum dependence of the diffuse coefficient Dp(p) has a maximum at Fermi momentum p = pF whereas the drift coefficient Kp(p) is negative and reaches a minimum at p ≈ pF. For a cold Fermi system the diffusion coefficient takes the nonzero value which is caused by the relaxation on the distorted Fermi surface at temperature T = 0. The numerical solution of the diffusion equation was performed for the particle-hole excitation in a nucleus with A = 16. The evaluated relaxation time τr ≈ 8.3 ⋅ 10-23 s is close to the corresponding result in a nuclear Fermi-liquid obtained within the kinetic theory.

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Magnetoresistance of gallium

Canadian Journal of Physics ◽

10.1139/p70-375 ◽

1970 ◽

Vol 48 (24) ◽

pp. 3021-3028 ◽

Cited By ~ 4

Author(s):

J. R. Cook ◽

W. R. Datars

Keyword(s):

Magnetic Field ◽

Relaxation Time ◽

Fermi Surface ◽

Temperature Dependence ◽

Effective Mass ◽

Field Direction ◽

Magnetic Field Direction ◽

Current Direction ◽

Rotation Curves ◽

Time Parameters

The magnetoresistance of gallium has been studied for b-axis current direction in fields up to 20 k0e. "Rotation curves" of magnetoresistance versus magnetic field direction exhibited both principal and subsidiary minima. These minima are discussed using the pseudopotential model of the Fermi surface and major topological dimensions of the sixth-band hole surface are measured using observed angular ranges of subsidiary minima. The principal minima result from the ka and kc open trajectories. The subsidiary minima are shown to occur by means of nonsaturating ka open trajectories, extended orbits, and [Formula: see text] effects involving local variations in both effective mass and relaxation time parameters. The temperature dependence of the magnetoresistance was measured for field directions in the ac plane. Relaxation time ratios derived through Kohler's rule are anisotropically scaled with temperature, indicating deviations from Kohler's rule.

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Theory of the temperature dependence of the Fermi-surface-induced splitting of the alloy diffuse-scattering intensity peak

Journal of Physics Condensed Matter ◽

10.1088/0953-8984/10/9/001 ◽

1998 ◽

Vol 10 (9) ◽

pp. L145-L151 ◽

Cited By ~ 5

Author(s):

Igor Tsatskis

Keyword(s):

Fermi Surface ◽

Temperature Dependence ◽

Diffuse Scattering ◽

Scattering Intensity ◽

Diffuse Scattering Intensity

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Macroscopic description of arbitrary Knudsen number flow using Boltzmann–BGK kinetic theory. Part 2

Journal of Fluid Mechanics ◽

10.1017/s0022112010001722 ◽

2010 ◽

Vol 658 ◽

pp. 294-309 ◽

Cited By ~ 1

Author(s):

HUDONG CHEN ◽

STEVEN A. ORSZAG ◽

ILYA STAROSELSKY

Keyword(s):

Relaxation Time ◽

Kinetic Theory ◽

Closed Form ◽

Knudsen Number ◽

Constitutive Models ◽

Spatial Dimension ◽

Scalar Transport ◽

Constant Relaxation Time ◽

Number Flow ◽

Short Times

We extend our previous analysis of closed-form equations for finite Knudsen number flow and scalar transport that result from the Boltzmann–Bhatnagar–Gross–Krook (BGK) kinetic theory with constant relaxation time. Without approximation, we obtain closed-form equations for arbitrary spatial dimension and flow directionality which are local differential equations in space and integral equations in time. These equations are further simplified for incompressible flow and scalars. The particular case of no-flow scalar transport admits analytical solutions that exhibit ballistic behaviour at short times while behaving diffusively at long times. It is noteworthy that, even with constant relaxation time BGK microphysics, quite complex macroscopic descriptions result that would be difficult to obtain using classical constitutive models or continuum averaging.

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